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Question

A box contains 6 red, 4 blue, 2 green and 4 yellow pencils.

If four pencils are picked at random, what is the probability that one is green, two are blue and one is red?

A 13/248 Correct Answer Incorrect Answer
B 18/455 Correct Answer Incorrect Answer
C 14/335 Correct Answer Incorrect Answer
D 12/545 Correct Answer Incorrect Answer
E none of these Correct Answer Incorrect Answer

Solution

Total number of pencils = 6 + 4 + 2 + 4 = 16 Let S be the sample space. Then, n(S) = number of ways of drawing 4 pencils out of 16 = 16C4 =`(16xx15xx14xx13)/(4xx3xx2xx1)` = 1820 Let E= event of drawing 4 pencils so that one is green, two are blue and one is red = n(E) = 2C1 X 4C2 X 6C1 = 2 `xx` 6 `xx ` 6= 72 [if gte msEquation 12]>∴ [if !msEquation]--> [endif]-->P (E) = `(n(E))/(n(S))=72/1820=18/455`

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